面内スピンバルブ素子における Hanle 効果

21 Hanle 2010 1 25 : 47-086046 :

Copyright 2010, Hiroki Nanaumi.

i 1 1 1.1................................... 1 1.1.1............................. 1 1.1.2............................ 1 1.2........................... 2 1.2.1........................ 2 1.2.2....................... 3 1.2.3............................... 4 1.2.4................................. 6 1.2.5.................. 7 1.2.6 Hanle................................. 10 1.3................................... 15 2 16 2.1................................... 16 2.1.1................................ 16 2.1.2................................. 18 2.1.3..................... 19 2.2...................................... 21 3 23 3.1 Py / Cu Hanle....... 23 3.2 Py / Al Hanle.................. 26 3.3 Hanle....................... 30 4 32 4.1 (Dwell time).................. 32 4.2 Py / Cu Hanle..... 33 4.3 Py / Al Hanle............... 35

ii 4.4 Hanle....................... 36 5 38 5.1................................... 38 5.2..................................... 39 42

1 1 1.1 1.1.1 e /( ) 1 (Giant magneto- Resistance:GMR) GMR (Tunnel Magneto Resistance:TMR) 2 *1 MRAM 3 (Magnetoresistive Random Access Memory) 1.1.2 GMR TMR *1 IBM:Data in the Fast Lanes of Racetrack Memory (SCIENTIFIC AMERICAN June 2009)

2 1 ( ) 1985 Johnson Silsbee 4 77 K *2 Jedema 5, 6, 7 Cu Al 1.2 1.2.1 Fe, Co, Ni 1.1 (p) p j j j + j (1.1) j j j C e j C j + j (1.2) j S j j (1.3) j S = p j C (1.4) *2 µm

1.2 3 (a) (b) E E EF N (E) Density of states N (E) N (E) Density of states N (E) 1.1. (a) (b) 1.1(b) p = 0 j S = 0 0 4 1.2.2 p ( 1.2) / 8

4 1 E E 1.2. 1.2.3 D, e N σ, σ, = e 2 N, D, (1.5) ( j, ) (E) (e > 0) (δn, ) j, = σ, E ed, δn, (1.6) (1.5)(1.6) j, = σ (, 1 ) ee δn, e N, (1.7) (δϵ, δn, N, ) µ ϵ + eϕ ϕ 1.7 j, = σ, e µ, (1.8) 9, 10 1.8 11 ( 1.3)

1.2 5 μ ( a) ( b) ( c) lf ln 1.3. (a) / (b) (c) τ, τ 0 = δn τ δn τ 1 e j 0 = δn τ δn τ 1 e j (1.9) N τ 12 D τ sf = N τ δ, = N, δϵ δϵ δϵ = µ µ D 2 (µ µ ) = 1 τ s f (µ µ ) (1.10) D = (N + N )D D N D + N D ( 1 τ sf = 2 + 1 ) 1 (1.11) τ τ 12 V S µ µ e = µ e (1.10) V S = V + exp ( x ) + V exp ( Dτsf x ) Dτsf (1.12)

6 1 Dτ sf λ Dτ sf ( 1.3) 11 1.2.4 () 1.4 (δµ) j S = j j スピン μ スピンと スピン 1.4. (a) (b)

1.2 7 1.2.5 ( a) スピン V ( ) μ b ( c) μ の の 1.5. (a) : (b) (c) Cu 100 nm / / ( 1.5)

8 1 j C = j + j = 0 µ σ x + σ µ x = 0 (1.13) (V p = µ/e) (V ap = µ/e) ( V S ) (I inj ) R S V S I inj Kimura 11 A ρ R S 2ρλ sf A 1 (1 P 2 ) (1.14) 5 nm A A Cu Al A *3 R S λ (1.6) (R series S ) R series S = R S1 sinh(d/λ 1 ) + R S2 cosh(d/λ 1 ) R S1 cosh(d/λ 1 ) + R S2 sinh(d/λ 1 ) R S1 (1.15) (R parallel S ) R Sparallel = R S1R S2 R S1 + R S2 (1.16) *3 Py Cu R Cu S = 2.6 Ω, RPy S = 0.34 Ω 11 Py Cu 8

1.2 9 (a) (b) DV0 d R S1, l1 R, l DV0 DV1 R S2, l2 S2 2 R S1, l1 (c) DV0 R N, l R, N l F F s2 R N, ln R N, l R, l F F s1 N 1.6. (a) (b) (c) 1.6(a) (T) T V S1 V S0 = R S2 R S1 sinh(d/λ 1 ) + R S2 cosh(d/λ 1 ) (1.17) 1.6(c) S1 R S1 R S1 = (1.15) S 2 R FR N R F + R N (1.18) R S = R N sinh(d/λ N ) + R S1 cosh(d/λ N ) R N cosh(d/λ N ) + R S1 sinh(d/λ N ) R N (1.19) (R S2 ) R All S2 = ( 1 R N + 1 R F + 1 R S2 ) 1 ( R F R N RF cosh(d/λ N ) + (R F + R N ) sinh(d/λ N ) ) = 2R F (R F + R N ) cosh(d/λ N ) + (2R 2 F + 2R FR N + R 2 N ) sinh(d/λ N) (1.20) / (T 2 ) (1.17) T 2 = R S1 R N sinh (d/λ N ) + R S1 cosh(d/λ N ) (1.21) V 2 V 2 = T 2 I S R S2 (p) ( R S ) R S = R 2 F R N(R F + R N + R F cosh(d/λ N ))p 2 (2R F + R N ) ( 2R F (R F + R N ) cosh(d/λ N ) + (2R 2 F + 2R FR N + R 2 N ) sinh(d/λ N) ) (1.22)

10 1 Takahashi 12 R S = 2R N ( P J 1 P 2 J ( 1 + 2 P J 1 P 2 J ) 2 R J R R N + p F F R N e d/λ N ) 2 R J R N + 2 R F R N e 2d/λ N (1.23) P J, R J (R J = 0) (1.22) (R J >> R N ) (1.23) R S = 1 2 R NP J exp( d/λ N ) (1.24) 13 1.2.6 Hanle Hanle Hanle s µ = γs B µ µ B ds dt = µ B ω L ω L = gµ BB g, µ B g (1.25) t ϕ = ω L t 1.7 cos(ϕ)

1.2 11 1.7 (a) B (b) B y z x 1 2 3 or I F1 F2 V (c) スピン ( V / I) 1 0 F1,F2 F1,F2 1 2 3-1 π 2π スピン ( φ) [rad] 1.7. ( δn δn δn ) δn t = D 2 δn x 2 δn τ SF (1.26) t = 0x = 0 14, 15 δn(x, t) = 1 4πDt exp ( x2 4Dt ) ( exp t ) τ SF (1.27)

12 1 (1.26) x = 0 ( 1.8) ( 1.9) スピン スピン t = t0 t = t1 P t = t2 x x=0 x=l 1.8. PI/Ae (1.27) n n n n = IP J ea = IP J ea 0 λ N 2D exp 1 dt exp 4πDt ( ) ( ( x2 exp t ) 4Dt τ SF ) (1.28) x DτSF µ µ = 2 N(ϵ F ) (n n ) V I = P2 J λ ( N σa exp x ) (1.29) λ N P J, A, σ (1.29)

1.2 13 P x=l t スピンをしない 2 1 x P exp 4Dt 4Dt スピンをした τ SF P 2 1 x t exp exp 4Dt 4Dt SF 1.9. x = L (1.29) (1.24) ω L t cos(ω L t) n n = IP J ea 0 0 dt ) ( 1 exp ( x2 exp t ) cos (ω L t) (1.30) 4πDt 4Dt τ S F 5 2 V I = P ) J 1 dt e 2 exp ( x2 exp N(ϵ F )A 4πDt 4Dt ( t τ S F ) cos (ω L t) (1.31) F 0 dt ) ( 1 exp ( x2 exp t ) cos (ω L t) (1.32) 4πDt 4Dt τ S F

14 1 F [ F = Re 0 dt 1 = Re 2 D 1 exp ( x2 4πDt 4Dt ( exp 1 L Dτ SF iω L 1 τ SF i ω L D ) ( exp t ) τ SF ) ] e iω Lt (1.33) (1.33) (1.34) 1.10 b ω L τ SF 2 L (1.34) l 2 λ N 1.10. l 2π 2π Hanle Hanle 16, 17 Hanle 18, 19

1.3 15 1.3 Hanle Hanle Hanle

16 2 2.1 λ 2.1.1 2.1

2.1 17 2.1. (a) (b) (c) (d) (e)

18 2 K-Cell Al Py,Co Cu (K-Cell) ( ) ( ) (トランスファーる) 2.2. 2.1.2 2.2 (LL)K-Cell *1 Cu K-Cell Al *2 1 10 9 TorrLL 1 10 7 Torr *1 Knudsen cell *2

2.1 19 2.3. PMMA/MMA 2 2.1.3 1. / 2. 3. 4. 4 Si/SiO 2 MMA() 180 C 3 PMMA() 180 C 10 8.8 C/m 2 MIBK( ) IPA() 1 : 3 30 IPA PMMA MMA 2.3 2.4(b) PMMA Cu 2.4 Cu Al

20 2 2.4. (a) 2 Si/SO 2 (b) (c) (d) (e) (a)(b)(e)

2.2 21 2.2 T = 10 K 4 2.5 4 He 1.5 K 10 K ポンプ He ( ヒーター ) 2.5.

22 2 2.6 2.7 ロックインアンプ オシレータ V- V+ プリアンプ A 2.6. ロックインアンプ オシレータ V- V+ プリアンプ A DC 2.7.

23 3 Hanle Hanle Hanle Hanle Hanle Hanle Py/Cu Al Hanle 3.1 Py / Cu Hanle Hanle (I) : (II) : 3.1 *1 ( Py ) λ Cu Py Cu *1 Ni 80 Fe 20

24 3 (a) 800 nm (b) (c) Py Py Cu Py Cu Cu Al2O3 3nm 100nm 30nm 100nm 30nm 3.1. SEM Py 800 nm Py,Cu 30 nm,100 nm (II) 3 nm 30 nm100 nm (II) Py Al 3 nm (20 Pa) 20 Al 2 O 3 *2 Py Py Py / 10 K Hanle *3 ( AMR ) ( 3.2) (a) (b) B (Ω) Py wire resistance 27.4 27.3 27.2 27.1 AMR effect @10 K 27-10 0 10 Magnetic field (KOe) I- I+ Py V- V V+ 3.2. AMR (a) Py (b) *2 Al *3 Anisotropic Magneto-Resistive effect

3.1 Py / Cu Hanle 25 (II) I-V I-V (II) ( (3.3)) (a) dv/di (Ω) 0.65 0.64 0.63 0.62 (b) V+ I- V- (c) Current (ma) 0.61 0.6 0.05 0-0.05-0.05 0 0.05 DC current (ma) I+ -0.05 0 0.05 Voltage (mv) 3.3. (a) (b) (c) I-V (I) (II) 0.06 Ω, 0.63 Ω (3.4) (II) Spin accumulation signal V/I (mω) 0.5 0 R -0.5 L= 800 nm @10 K -1-1 0 1 Magnetic field (KOe) ( I) R = 0.1 (m Ω) ( II) R = 1.6 (m Ω) 3.4. Py / Cu ( R)

26 3 Hanle Py (3.1) 1 3.5 (I) (II) V(, θ 1, θ 2 ) = V B cos θ 1 cos θ 2 + V(B = 0) sin θ 1 sin θ 2 (3.1) θ 1, θ 2 AMR Hanle signal (normalized) 0.4 0.2 0-0.2-0.4 Py / Cuスピンバルブ @ 10 [K] R ( I) ( II) I- V- B -2-1 0 1 2 Magnetic field (koe) I+ V+ 3.5. (I) (II) Hanle Hanle B = 0 3.2 Py / Al Hanle Py / Cu Al Py Al Al 60 nm (20 Pa, 20 ) Al Py 40 nm ( 3.6(b)) Py 30 nm Al 60 nm ( 3.6(a))Al ( 3.6(c))

3.2 Py / Al Hanle 27 (a) Al (b) Al Py Py Py 1 μ m 1 μ m (c) グレイン 3.6. (a)py/al (b)py/al (c) Al (a) V (b) 1135 Py / Al tunnel @10 K Tunnel I dv/di (Ω) 1134 1133 1132 V- I- V+ Py Cu I+ +DC 1131-0.01 0 0.01 DC current (ma) 3.7. (a)i-v (b)py / Al

28 3 Py / Al I-V 3.7 (dv/di) Al Hanle AMR Py Py B, B S sin θ = B/B S (3.1) V(B ) = V B (1 (B /B S ) 2 ) + V(B = 0)(B /B S ) 2 (3.2) λ = Dτ SF = 640 nmal R Al S = 7.90 Ω*4 Hanle 3.9 Hanle Py / Cu Py / Al Hanle ( 3.11) Spin accumulation signal (m Ω ) 4 3 2 1 0 L = 950 nm @ 10 K 0 5-5 Magnetic field (koe) data Fitting 3.8. () Hanle () ρ Al = 6.14 10 8 µωcm τ SF = 90 ps, D = 4.6 10 3 m 2 s 1, P J = 0.091 Al λ = DτSF = 640 nm AMR B S = 6.0 koe *4 150 nm 60 nmρ Al = 6.14 10 8

3.2 Py / Al Hanle 29 Hanle signal (normalized) 0.6 0.4 0.2 Py / Al スピンバルブ @10 K R/2 オーミック L= 800 nm トンネルフィット トンネル L= 950 nm 0-2 -1 0 1 2 Magnetic field (koe) 3.9. Py/Al Hanle Hanle B =0 150 nm Al Py Hanle signal (normalized) 0.5 0.4 0.3 0.2 0.1 L= 800 nm @ 10 K R/2 Py / Cu オーミック Py / Al オーミック 0-4 -2 0 2 4 Magnetic field (koe) 3.10. Py/Al Py/Cu L = 800 nm Hanle

30 3 3.3 Hanle Py / Cu Py / Al Hanle *5 Py Hanle Py(R Py S = 0.12 Ω *6 ) Co(R Co S = 1.40 Ω *7 ) Hanle L = 800 nm *8 Cu Co 100 nm, 30 nm 800 nm Cu Cu Co 100nm 30nm 3.11. Co / Cu SEM Co, Cu 100nm, 30 nm *5 spin sink effect *6 ρ Py = 12.20 µωcmλ Py =5 nm A = 100 100 nm 2 *7 ρ Co = 14 µωcm λ Co = 50 nm A = 100 100 nm 2 *8 Co

3.3 Hanle 31 10 K Cu ρ Cu = 1.07 µωcm Co / Cu 0.03 Ω 0.04 mω Py / Cu 0.1 mω ( 3.4) Hanle 14 KOe Co *9 Co Hanle Py / Cu ( 3.12) Hanle signal (normalized) 0.5 0.4 0.3 0.2 0.1 L=800nm @10 K R/2 Py / Co オーミック Py / Cu オーミック 0-4 -2 0 2 4 Magnetic field (koe) 3.12. Co / Cu Py / Cu Hanle *9 CoPy 30 koe10 KOe 20

32 4 Hanle 4.1 (Dwell time) τ D j e n v j = env σ =, j D = ed n σ x *1 v σ = D 1 n σ n σ x (4.1) n (x)n (x) n σ = n +,σ exp ( x + n,σ exp λ) ( x ) λ (4.1) n +,σ = N 0 2 (1 α), n,σ = N 0 2 (1 + α), N 0 = n +,σ + n,σ (4.2) α = (R SN + R SI + R SF ) cosh( L λ ) + (R SI + R SF ) sinh( L λ ) (R SN + R SI + R SF ) sinh( L λ ) + (R SI + R SF ) cosh( L λ ) (4.3) *1 (1.6) E =0

4.2 Py / Cu Hanle 33 R SN, R SI, R SF L L RSN RSI RSN RSI RSN RSF RSF 4.1. (4.2) 1 (R SI R SF, R SN ) n +,σ = 0 (R SI = 0) n +,σ < 0 (4.1) (4.4) v σ = D 1 n σ n σ x = D λ (n +,σ exp( x λ ) n,σ exp( x λ ) ) n +,σ exp( x λ ) + n,σ exp( x λ ) (x = 0) (x = L) (τ D ) L dx τ D = 0 v = λ D L + λ ln n n + n n + exp( 2L λ ) = λ D L + λ ln (R SN + R SI + R SF ) cosh ( ) L λ + (RSI + R SF ) sinh ( ) L λ (R SN + R SI + R SF ) ( sinh ( ) ( )) L λ + cosh L λ (4.5) τ D (4.4) (4.5) 4.2 Py / Cu Hanle ( (I)) ( (II)) Hanle 3.5 (I) Hanle (II) Hanle Dwell time (τ D )

34 4 (I) τ D = 24 ps (II) τ D = 34 ps *2 Dwell time Hanle R SI (I) 0.06 Ω (II) 0.63 Ω 10 τ D ( 4.2) (4.5) R SI ln L τ D L 800 nm 80 70 Dwell time (ps) 60 50 40 30 35 30 25 ( I) ( II) 0.0 0.2 0.4 0.6 0.8 0 10 20 30 40 R SI ( Ω) 4.2. (4.5) Dwell time (R SI ) Dwell time R SN = 3.21 Ω, R SF = 0.122 Ω, λ = 1500 nm, L = 800 nm, D = 0.015 m 2 s 1 R SI = 0 *2 λ Cu = 1500 nm, D=0.015 m 2 s 1, R SF = 0.122 Ω, ρ Cu = 1.07 µωcm

4.3 Py / Al Hanle 35 4.3 Py / Al Hanle Py / Cu Py / Al Py / Al Py / Cu Hanle 3.9 Py/ Al Hanle (4.5) (R SI = 0) (R SI R SF, R SN ) τ D τ Ohmic D τ Tunnel D R SI =0,R SN R SF λl D R SI R SF,R SN λl D 1 + ln cosh ( ) L λ cosh ( L λ ) + sinh ( L λ 4.3 λ τ SF Dwell time 4.3 2 オーミック トンネル ) (4.6) τd τsf 1 Py / Al トンネル Py / Al オーミック Py / Cu オーミック 0 0 1 2 4.3. Dwell time (x/λ) Dwell time (τ D /τ sf ) τ Cu sf = 150 psτ Al sf =90 psl = 800 nmλ Al = 640 nmλ Cu = 1500 nm

36 4 Hanle (4.4) Hanle スピン μ L μ L L トンネル オーミック 4.4. 3.10 Py / Cu Py / Al Hanle τ D Al Cu R Al = 7.9 Ω *3 R Cu = 3.2 Ω *4 Al τ D (4.5) Al Cu τ D τ Al D = 58 ps = 24 ps τ Cu D τ D Py / Cu Py / Al 21 4.4 Hanle Py τ D *3 λ Al = 643 nmρ Al = 5.88 µωcm *4 λ Cu = 1500 nmρ Cu = 1.07 µωcm

4.4 Hanle 37 Co τ D 3.12 τ D Py Co τ Py D = 24 ps τco D = 37 *5 ps 10 ps τ D Hanle Co Py Hanle *5 R Co = 1.4 Ω

38 5 Hanle 5.1 1. Hanle Hanle Hanle 2. 3. Hanle ahanle bhanle chanle τ D Hanle Hanle

5.2 39 5.2 Hanle Hanle Hanle Hanle

40 [1] T. Valet and A. Fert, Theory of the perpendicular magnetoresistance in magnetic multilayers, Phys. Rev. B 48(10), 7099 7113 (1993). [2] Julliere, Tunneling between ferromagnetic films, Phys. Lett. A 54A(3), 225 226 (1975). [3] S. Tehrani and e. al, Magnetoresistive random access memory using magnetic tunnel junctions, Proceedings of the IEEE 91(5), 703 714 (2003). [4] M. Johnson and R. H. Silsbee, Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals, Phys. Rev. Lett. 55(17), 1790 1793 (1985). [5] F. J. Jedema. Electrical spin injection in metallic mesoscopic spin valves. PhD thesis, the University of Groningen, (2002). [6] F. J. Jedema, A. T. Filip, and B. J. van Wees, Electrical spin injection and accumulation at room temperature in an all-metal mesoscopic spin valve, Nature 410(1), 345 348 (2001). [7] F. J. Jedema, H. Heersche, A. Filip, J. Baselmans, and B. van. Wees, Electrical detection of spin precession in a metallic mesoscopic spin valve, Nature 416(2), 713 716 (2002). [8] D. Steiauf and M. Fähnle, Elliott-Yafet mechanism and the discussion of femtosecond magnetization dynamics, Phys. Rev. B 79(R), 140401 (2009). [9] M. A. M. Gijs and G. E. W. Bauer, Perpendicular giant magnetoresistance of magnetic multilayers, Adv. Phys. 46(3), 285 445 (1997). [10] P. C. van Son, H. van Kempen, and P. Wyder, Boundary Resistance of the Ferromagnetic- Nonferromagnetic Metal Interface, Phys. Rev. Lett. 58(21), 2271 2273 (1987). [11] T. Kimura, J. Hamrle, and Y. Otani, Estimation of spin-diffusion length from the magnitude of spin-current absorption: Multiterminal ferromagnetic/nonferromagnetic hybrid structures, Phys. Rev. B 72(1), 014461 (2005). [12] S. Takahashi and S. Maekawa, Spin injection and detection in magnetic nanostructures, Phys. Rev. B 67(5), 052409 (2003). [13] E. I. Rashba, Theory of electrical spin injection: Tunnel contacts as a solution of the conductivity mismatch problem, Phys. Rev. B 62(24), R16267 R16270 (2000). [14] S. Zhang and P. Lavy, Time dependence of spin accumulation and magnetoresistance in magnetic multilayers, Phys. Rev. B 65, 052409 (2002).

41 [15] B. Huang and I. Appelbaum, Spin dephasing in drift-dominated semiconductor spintronics devices, Phys. Rev. B 77, 165331 (2008). [16] M. Johnson and R. H. Silsbee, Spin-injection experiment, Phys. Rev. B 37, 5326 (1987). [17] M. Johnson and R. H. Silsbee, Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals, Phys. Rev. Lett. 55(17), 1790 1793 (1985). [18] B. Huang, H.-J. Jang, and I. Appelbaum, Geometric dephasing-limited Hanle effect in longdistance lateral silicon spin transport devices, Appl. Phys. Lett. 93, 162508 (2008). [19] J. Li, B. Huang, and I. Appelbaum, Oblique Hanle effect in semiconductor spin transport devices, Appl. Phys. Lett. 92, 142507 (2008). [20].., (1960). [21] N. Theodoropoulou, A. Sharma, R. Loloee, P. J. Pratt, W., and J. Bass, Interface specificresistance and scattering asymmetry of permalloy/al, J. Appl. Phys. 99(9), 08G502 (2006).

42 (:)

Hanle